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Updated tutorial
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‎Python_Basics/Prime_Numbers/.ipynb_checkpoints/PrimeNumbers-TimeComparison-checkpoint.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This is where to show how long it takes to run each method. "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Method 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"metadata": {},
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"outputs": [],
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"source": [
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"primes = []\n",
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"for num in range(2, 20 + 1):\n",
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" isPrime = True\n",
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" for y in range(2, num):\n",
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" if num % y == 0:\n",
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" isPrime = False\n",
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" \n",
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" if isPrime:\n",
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" primes.append(num)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[2, 3, 5, 7, 11, 13, 17, 19]"
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]
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},
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"execution_count": 25,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"primes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Method 2"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Only difference is a break statement. Basically once you know that a number isn't prime why should you keep on testing it in the inner loop"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"metadata": {},
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"outputs": [],
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"source": [
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"primes = []\n",
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"for num in range(2, 20 + 1):\n",
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" isPrime = True\n",
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" for y in range(2, num):\n",
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" if num % y == 0:\n",
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" isPrime = False\n",
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" break\n",
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" \n",
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" if isPrime:\n",
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" primes.append(num)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[2, 3, 5, 7, 11, 13, 17, 19]"
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]
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},
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"execution_count": 27,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"primes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Method 3"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"When you are testing whether a nuber is prime, all you are doing is testing whether a number times another number is prime. Eventually you will get to a situation where you will multiply the same prime numbers against each other. \n",
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"\n",
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"Commutative property: When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example 4 * 2 = 2 * 4"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"6 x8 is the same as 8 x 6 (can make a visual on this). The image above is all the factors for 48 (notice it gets repetitive). up a hill and down. communtative property of multiplication). Tipping point happens at the square root of a number."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 30,
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"metadata": {},
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"outputs": [],
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"source": [
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"primes = []\n",
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"for x in range(2, 20 + 1):\n",
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" isPrime = True\n",
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" for y in range(2, int(x ** 0.5) + 1):\n",
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" if x % y == 0:\n",
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" isPrime = False\n",
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" break\n",
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" \n",
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" if isPrime:\n",
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" primes.append(x)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 31,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[2, 3, 5, 7, 11, 13, 17, 19]"
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]
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},
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"execution_count": 31,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"primes"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python [conda root]",
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"language": "python",
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"name": "conda-root-py"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.4"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

‎Python_Basics/Prime_Numbers/.ipynb_checkpoints/PrimeNumbersPython-checkpoint.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Method 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"metadata": {},
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"outputs": [],
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"source": [
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"primes = []\n",
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"for num in range(2, 20 + 1):\n",
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" isPrime = True\n",
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" for y in range(2, num):\n",
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" if num % y == 0:\n",
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" isPrime = False\n",
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" \n",
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" if isPrime:\n",
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" primes.append(num)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[2, 3, 5, 7, 11, 13, 17, 19]"
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]
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},
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"execution_count": 25,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"primes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Method 2"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Only difference is a break statement. Basically once you know that a number isn't prime why should you keep on testing it in the inner loop"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"metadata": {},
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"outputs": [],
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"source": [
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"primes = []\n",
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"for num in range(2, 20 + 1):\n",
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" isPrime = True\n",
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" for y in range(2, num):\n",
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" if num % y == 0:\n",
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" isPrime = False\n",
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" break\n",
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" \n",
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" if isPrime:\n",
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" primes.append(num)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[2, 3, 5, 7, 11, 13, 17, 19]"
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]
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},
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"execution_count": 27,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"primes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Method 3"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"When you are testing whether a nuber is prime, all you are doing is testing whether a number times another number is prime. Eventually you will get to a situation where you will multiply the same prime numbers against each other. \n",
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"\n",
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"Commutative property: When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example 4 * 2 = 2 * 4"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"6 x8 is the same as 8 x 6 (can make a visual on this). The image above is all the factors for 48 (notice it gets repetitive). up a hill and down. communtative property of multiplication). Tipping point happens at the square root of a number."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 30,
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"metadata": {},
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"outputs": [],
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"source": [
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"primes = []\n",
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"for x in range(2, 20 + 1):\n",
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" isPrime = True\n",
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" for y in range(2, int(x ** 0.5) + 1):\n",
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" if x % y == 0:\n",
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" isPrime = False\n",
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" break\n",
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" \n",
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" if isPrime:\n",
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" primes.append(x)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 31,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[2, 3, 5, 7, 11, 13, 17, 19]"
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]
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},
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"execution_count": 31,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"primes"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python [conda root]",
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"language": "python",
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"name": "conda-root-py"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.4"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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